Physical atomistic kinetic Monte Carlo modeling of Fermi-level effects of species diffusing in Silicon

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1 Physical atomistic kinetic Monte Carlo modeling of Fermilevel effects of species diffusing in Silicon I. MartinBragado, P. Castrillo, M. Jaraiz, R. Pinacho, J.E. Rubio, and J. Barbolla Department of Electronics, University of Valladolid. ETSIT Campus M. Delibes, 4711 Valladolid, Spain (Dated: October 21, 24) An accurate physicallybased Fermilevel modeling approach, amenable to be implemented in an atomistic devicesize process simulator, is reported. The atomistic kinetic Monte Carlo method is used for point and extended defects, in conjunction with a quasiatomistic, continuum approach treatment for carrier densities. The model implements charge reactions and electric bias according to the local Fermilevel, pairing and breakup reactions between particles, clusteringrelated dopant deactivation and Fermi leveldependent solubility. We derive expressions that can be used as a bridge between the continuum and the atomistic frameworks. We present the implementation of two common dopants, Boron and Arsenic, using parameters that are in agreement with both abinitio calculations and experimental results. I. INTRODUCTION II. PHYSICAL MODELS Current microelectronic technology is facing increasingly complex phenomena related to very highdoping, reduced thermal budget (nonequilibrium conditions), and three dimensional effects. Such conditions require a deep insight into the underlying physical mechanisms in order to correctly model the material properties. In particular, highdoping concentrations demand a correct description of diffusion under extrinsic conditions. 1,2 Other chargerelated issues are Fermilevel dependent solubility, 3,4 clusteringrelated dopant deactivation, 5 and highdamage electrical compensation. Continuum modeling, based on solving partial differential equations (PDE) discretized by the finite element method, has been used since the 198 s, but this method is limited by the number of equations that can be solved without running into convergence instabilities. Moreover, meshing issues and dimensionality make this approach extremely complicated in 3D. The International Roadmap for Semiconductors 23 6 establishes the Modeling hierarchy from atomistic to continuum among the difficult challenges that need to be solved before 21. The atomistic kinetic Monte Carlo (kmc) method, 7 has proven to be a powerful approach that allows the inclusion of comprehensive, physically based models without significantly degrading the simulator s performance. Some semiconductor companies 8,9 and software vendors 1,11 have already started to develop simulators based on this atomistic kmc approach. Modelling Fermi level effects is one of the critical steps in developing a comprehensive kmc simulator. Here we will describe a detailed Fermilevel modeling approach specially designed to be included in this methodology, which has been implemented and tested in the atomistic kmc process simulator DADOS. 12 We first describe in detail the basic physical models and then the particular implementation of point defects and of two representative dopants (boron and arsenic), and finally show a simulation example. In this section we will introduce some concepts not explicitly present in continuum models which will allow us to adapt the formulation of Fermilevel effects in diffusion 1 to an atomistic framework. In our simulation scheme, particles are represented atomistically, with a particular position, species, type (substitutional, interstitial) and charge. Defects are formed by such particles. Electrical equilibrium can be assumed even when particle concentrations are far from equilibrium conditions because the charge reactions are much faster than structural reactions. 13 As a consequence, the Fermilevel (e F ) is considered to be well defined and carrier concentrations are treated in a continuum fashion. A. Concentrations of charged states Let us consider a particle X as an example of native point defect (self interstitials, I, or vacancies, V ) in silicon, which is the focus of our study. They can be in multiple charge states X j, with j =,,, +, ++. We denote by e(j + 1, j) the energy level associated to the charge transitions between X j+1 and X j. Then, the relative concentrations are: [X j ( ) ] [X j+1 ] = gj ef e(j + 1, j) exp (1) gj+1 kt g j being the degeneracy factor and kt the thermal energy. We assume the same degeneracy factor for all the charge states. Our convention is to take the origin of energy levels at the valenceband edge. We can assume that the electric levels of all charged species vary with the temperature proportionally to the band gap width E g. 14 The concentration of neutral native point defects (I or V ) in equilibrium conditions, denoted as [X ], is controlled by its formation energy, E f (X ), that is independent of e F. From Eq. 1 one can derive the concentration

2 2 of charged states and their formation energies. The total point defect concentration as a function of e F will be primarily determined by the charge state with lower E f. For e F = e(j + 1, j) the formation energies of X j+1 and X j are the same and therefore [X j+1 ] = [X j ]. Since there are no explicit assumptions of equilibrium in Eq. 1 it is still valid out of equilibrium, and then the supersaturation, defined as S X = [X]/[X], is the same for all the charge states: E m ν +x ν x [X j ]/[X j ] = [X ]/[X ] = S X. B. Defect diffusivities In atomistic kmc, defect diffusivity is related to the random walk of migrating defects. The point defect migration frequency ν m for a given charge state j of a particle X is: ν m (X j ) = ν m, (X j ) exp( E m (X j )/kt ) (2) ν m, being the migration prefactor and E m the migration energy. Accordingly, in three dimensions, D(X j ) = λ 2 ν m (X j )/6, (3) where λ is the jump distance. We have chosen λ to be equal to the second neighbors distance in the silicon lattice (.384 nm). The transport capacity due to diffusion will be DC(X) = j D(Xj )[X j ]. Under equilibrium conditions the products D(X j )[X j ] are going to have an activation energy of (X j ) = E m (X j ) + E f (X j ), denoted as diffusion energy. The transport capacity will be dominated by the charge state with lower. C. Electric drift Fig. 1 shows electric drift as a natural consequence of the local dependence of the formation energies of charged particles. Within the kmc framework, the relation between the migration frequency in the positive and negative directions along the x axis for a point defect with charge jq is ( ν m,+x = exp λ ν m, x kt ) de f = exp dx ( ) jqex λ kt (4) where E is the electric field and q is the absolute value of the electron charge. The last equality assumes constant band gap. From Eq. 4 one can derive the xcomponent of drift velocity to be equal to v x = λ(ν m,+x ν m, x )/6 which, in a first order approximation, becomes the Einstein relation v x = jqde x /(kt ). jq E x λ λ E (x) f FIG. 1: Electric drift within a kmc framework (see Eq. 4). D. Point defect reactions Reactions between particles take place in kmc when particles are within the capture radius of each other. In our model two different reactions are implemented: pairing with impurities (A) and break up, X j + A k AX j+k (5) conserving the charge, and reactions of equilibrium between different charge states X j+1 + e X j. (6) The pairing reactions between repulsive species are forbidden. For the break up reactions, due to the charge conservation, ν bk does not depend on e F. Eq. 5 together with Eq. 6 are enough to take into account the different break up paths because we assume that the equilibrium between different charge states is instantaneous. In the present model clusters are assumed to be neutral and only neutral particles are emitted and captured. Once the neutral particle has been emitted as a point defect, it can change its charge state according to the local Fermi level. It would be easy to implement extended defects charge states in kmc, but reliable values for physical parameters (either from calculations or experiments) would be needed. E. Solubility The solubility of charged species depends on e F. 3,4 For the case of a dopant A j, the solubility limit is given by: ( [A j ] max (T ) = [A j ] intrinsic max (T ) exp j e ) i e F, (7) kt where [A j ] intrinsic max = ([Aj ] extrinsic max ) 2 n i (8)

3 3 is the solubility in intrinsic conditions (e F = e i ) and [A j ] extrinsic max the solubility when [A j ] max n i. Eq. 7 is a consequence of the fact that the formation energy of charged defects depends on e F. In an atomistic framework expression 7 can be fulfilled by trapping and emitting only neutral particles of the type AX with an emission rate independent of e F. F. Implementation Energies (ev) Implemented species I V As i As V (,) (,) (+,) (,) (,) (,) (+,) (+,) (++,+) (+,) (+,) E C E V Physical mechanisms involving defects can be described as interactions (reactions between two defects when they are within a capture radius) or as events (performed by defects with a certain frequency). The model described here has been implemented in the atomistic simulator DADOS. 1,12,15 The main tasks that the simulator has to do, related to charged pointdefects, are to maintain the right local ratio between the various charge states (Eq. 1), to compute the Fermi level (and thus the carrier concentration) and to include the electric bias effects (Eq. 4). Once the drift is properly accounted in equilibrium, [V ] and [I ] are constant even if e F. We calculate e F within the charge neutrality approximation and using the FermiDirac statistic, Bandgap narrowing 16,17 and damage induced electrical compensation. III. POINT DEFECTS: INTERSTITIALS AND VACANCIES A. Vacancies The charge levels for vacancies (V ++, V +, V, V and V ), are well characterized, 1,18 and they are represented in Fig. 2. The dependence of the formation energies with e F for charged vacancies using the values of table I are displayed in Fig. 3a (dashed lines). Thick dashed lines correspond to the most stable charge state (lower formation energy and higher concentration) that depends on the Fermi level. As it can be seen V + is a metastable state, i.e. it is not the minimum E f for any value of e F. [V ], that is constant with e F, is dominant for pdoped materials and of the same order as [V ] for intrinsic silicon. The solid lines are the diffusion energies. E m is different for each charged species, but we assume it does not depend on e F. The parameters displayed in Table I and represented in Fig. 3a has been chosen to correctly fit the vacancy transport capacity reported in Ref. 19 as well as the charge levels of Refs. 1,18. The Arrhenius plot for vacancy transport capacity with the contribution of different charge states is represented in Fig. 4a. FIG. 2: Electronic levels for V, I,, AsV and As i. B. Interstitials The charge levels of silicon selfinterstitials (I, I, I +, I ++ ), are not conclusively established. 1,18,2 Theoretical calculations indicate that I + is metastable but with a very low migration energy and controls interstitial diffusion for pdoped and intrinsic materials. 2,21 However, experiments show that in intrinsic silicon, diffusion is dominated by I, and I + dominate only for e F <.4. 1,22,23 As a simplification, and following Ref. 1, we will ignore the I ++ state in our model, and we believe it is not necessary for continuum models as well. Therefore we will describe the interstitial using the I +, I, I states. As we will see later (Sec. V), I ++ presence will not change dopant diffusivity, and it only has a very small contribution to long hop distance of dopants. The values of charge levels are taken from Ref. 1. Fig. 3b shows the formation and diffusion energies diagram that we have set for interstitials, listed in Tab. I. As commonly assumed, I is the dominant state near the intrinsic conditions and I only has a significant contribution for heavy ndoped materials. Theoretical calculations give a migration energy for neutral interstitials of about 1 ev, so we have taken E m = 1. ev for I and we have assumed the same value for the other charge states. These parameters fit experimental data for interstitial diffusivity in intrinsic silicon. 24,25 Figure 4b shows the Arrhenius plots for silicon selfinterstitial transport capacity. The experimental points (symbols) have been extracted from Ref. 24 and 25. The lines have been calculated using the parameters displayed in table I. IV. PAIR POINTDEFECTS: BORON AND ARSENIC Once the point defects, I and V, have been introduced, we will focus our study in the diffusion of dopants. Substitutional impurities are assumed to be immobile. Let us consider now the cases in which the migrating defect can be seen as the pair AX, where A is an impurity and

4 4 I I I + V V V V + V ++ B i B i B + i As i As + i AsV AsV AsV + D m, 1 3 (cm 2 /s) E m (ev) e t(t = ) (ev) [X ] ( 1 25 cm 3 ) E f (ev) TABLE I: Parameters used for charged states of silicon vacancy (V j ), silicon selfinterstitial (I j ), interstitial boron (B j i ) and vacancy and interstitial arsenic (AsV j, As j i ). D is the diffusivity prefactor (Eq. 3), Em the migration energy, and et the charge level measured from the valence band edge. For T, we assume that e t scales with band gap energy. 14 Prefactors for equilibrium concentrations and formation energies of I and V are also shown. Other parameters used in this work are, for boron: D bk, (B i ) =.4 cm2 s 1, E b (B i ) =.1 ev and for arsenic: D bk,(asv + ) = cm 2 s 1, E b (AsV + ) = 1 ev and D bk, (As + i ) = cm 2 s 1, E b (As + i ) =.1 ev. D bk, is the breakup prefactor expressed in diffusivity units (= (λ 2 /6) ν bk, ). D bk, and E b (T ) can be obtained from Eqs. 11 and 12. The point defect capture volume is 2λ 3. a) b) Energies (ev) int e(+,++) V + V ++.2 V.4 e(,) V V.6 e F (ev).8 V e(,) E g V 3.5 E f 3 1 V 1.2 Energies (ev) int I + I + e(,+) I I E m e(,) e F (ev) I I E g FIG. 3: Formation energies (E f, dashed lines) and diffusion energies ( = E f + E m, solid lines) of charged Silicon vacancy (a) and selfinterstitial (b) as a function of Fermilevel (e F ) using the parameter set of TableI. e F is measured from the valence band edge. (Bandgap energy is E g = 1.17 ev for T= K). Minimum values of E f and are drawn with thick lines. Edif int corresponds to the diffusion energy for intrinsic Silicon (e F = e i). Open circles indicate the energy crossings corresponding to charge levels. X is either an I or a V. We will describe first the diffusion of boron using and later the case for Arsenic with AsV and As i. A. Boron It is commonly accepted that B migrates mainly due to interstitial mechanism, via (either as an interstitial or a BI pair), rather than via V mediated mechanism. The known charged states of are B i, and B+ i.26 The three states are included in our model, although the inclusion of B + i will only show up for systems far from equilibrium. The pairing, break up and charge reactions related to are represented by the reactions I +B B i I + +B Bi B + i. (9) In the following, we assume that substitutional boron is always immobile and ionized (B ). In Eq. 9 horizontal reactions (pairing and breakup) conserve the charge while vertical reactions establish the electrical equilibrium. The rate of the horizontal reactions will not depend on the Fermilevel. Direct breakup of B + i is not included because I ++ is not implemented. The charge level values for are listed in table I and illustrated in

5 5 1e13 1e14 Temperature o C Experimental Our model 1e12 1e14 Temperature o C Cowern Bracht Our model (cm 2 s1) DC V rel 1e15 1e16 1e17 1e18 (cm 2 s1) DC I rel 1e16 1e18 1e2 1e22 1e24 1e e /T (K 1 ) a) 1 4 /T (K 1 ) b) FIG. 4: Arrhenius plots for the relative transport capacity (DC /[Si]) for a) V and b) I in intrinsic conditions. The parameters are set to fit the experimental data for I 24,25 and V. 19 E m (I ) E bk ( ) E b ( ) E m ( ) E f ( ) Ef (B ) v capt being the effective capture volume for pairing reaction and ν bk the breakup frequency. The ratio of Eq. 1 is independent of e F because the charges of B i and B are the same. In contrast, [Bi ]/[B ] and [B + i ]/[B ] are Fermilevel dependent. The activation energies of the [B j i ]/[B ] fractions are represented as formation energies in Fig. 6. The activation energy for B i breakup will be E b (B i ) + E m(i ) (see Fig. 5), E b denoting the binding energy. Considering energy conservation in reactions of Eq. 9 we obtain E b (B i ) = E b (B i ) + e (, ) e I (+, ) (11) E f (I ) FIG. 5: Potential energy diagram showing the formation and migration energies for B i and I, and the B i binding and break up energies. Fig. 2. These values have been measured by electrical characterization. 18,27,28 From the first reaction in Eq. 9 the number of broken B i per unit of volume and time will be [B i ]ν bk(b i ) and the number of new formed [B ][I ]ν m (I )v capt. Consequently, in local equilibrium conditions [B i ] [B ] = [I ] ν m(i ) ν bk (B i )v capt, (1) and the activation energy for Bi breakup will be E b (Bi ) + E m(i + ). Electronic levels scale with E g, introducing a slight T dependence in Eb(Bi ). From equilibrium conditions it can be also derived that the breakup prefactors, ν bk,, have to fulfil ν bk, (B i )/ν bk, (B i ) = ν m,(i + )/ν m, (I ). (12) Boron effective diffusivity D(B) is given by the sum of the contribution of all mobile species D(B) = D(B i )[B i ] [B ] +D( ) [ ] [B ] +D(B+ i ) [B+ i ] [B ]. (13) The diffusion energy value for boron under intrinsic conditions in Fig. 6 (Edif int ) will be similar to the activation energy of the Arrhenius plot of equilibrium boron diffusivity. The small differences can be attributed to the charge states and the modification of the charge levels with temperature. The activation energies of the terms in previous Equation (usually known as defectassisted diffusion energies or just diffusion energies, (B j i ))

6 6 e i e(,) e(,+) E g scopic parameters are therefore Energies (ev) 4 int E m ( + ) E m ( ) e F (ev).8 E f E m ( ) FIG. 6: Dashed lines: Energy to form a B j i from a B (E f (B j i ) E f (B )) as a function of Fermilevel using the values of TableI. Solid lines: Activation energy of the contribution of B j i for the effective Boron diffusivity in equilibrium conditions, (see Eq. 13). Migration energies (E m(b j i )) are the differences between solid and dashed lines. Black dot indicates the value of Edif int. The other notations correspond to Fig are represented in Fig. 6. From this Figure it can be seen that Bi is a metastable state (as e B + > e i B ) but is the i main contributor for boron diffusion in a wide range of e F and in consequence D(B) p/n i (Ref 2). According to Fig. 6 the effective migration energy of a for e F e i is (Bi ) E f (B + i ).6 ev, in agreement with the experimental observation. 26 It is also noticeable, that one can have D P P with no I ++. Actually, D(B) does not depend on the charge states of I, but on those of. The parameters listed in Table I and used in Fig. 6 have been chosen to fit the Arrhenius plot of equilibrium boron diffusivity, D(B) reported in Ref. 29. In particular, the binding energy of B i and migration energy of B i have been taken to fit the boron diffusivity Arrhenius plot, and the migration energies for B i and B + i are in agreement with the picture derived from abinitio calculations 3 and the experimental D (B) for n type silicon. 2 Using the Maxwell Boltzmann approximation, Eq. 13 is usually written in continuum models as : D(B) = S I [D X (B) + D P (B) p ( ) ] 2 p + D P P (B), n i n i (14) S I being the interstitial supersaturation, and p and n i the hole concentration and the intrinsic concentration, respectively. The relations between the above diffusivity components D X (B), D P (B), D P P (B) and the micro D X (B) = v capt D(I )[I ] ( ν m (B i )/ν bk(b i )) D P (B) = v capt D(I )[I ] ( ν m (Bi )/ν bk(b i )) exp ( (e Bi (, ) e i )/kt ) D P P (B) = v capt D(I )[I ] ( ν m (B + i )/ν bk(b i )) exp ( (e Bi (, ) + e Bi (+, ) 2e i )/kt ) (15) e i being the intrinsic level. These expressions can be used as a bridge between the parameters of continuum simulators and those of a kmc simulator. Nevertheless, the above continuum expression assume MaxwellBoltzmann and quasiequilibrium conditions, which are not needed within the kmc approach. We should point out that the above terms only depends on D(I ) without dependences on I + or I. The ratios ν m (B j i )/ν bk(b i ) mean that the diffusivity of each term can be increased by increasing the migration rate, or decreasing the break up rate, but increasing or decreasing both leaves the magnitude unchanged. The atomistic meaning is that the B diffusivity does not depend on how fast moves, but on the distance traveled (long hop) by the before breaking up. For slightly doped material, the dominant diffusing interstitial is I, which upon interaction with substitutional boron creates a B i which in turn switches to B + i very quickly because B + i has the lowest formation energy for these conditions. However, B + i is a slow diffusant that can also switch to Bi, which is a fast diffusant and provides the main contribution to the overall boron diffusivity. Notice that the most frequent break up reaction is for the B i charge state to fulfil microscopic reversibility of the most frequent pairing reaction. B. Arsenic Once boron charged states have been explained, a similar analysis can be done for arsenic, which has both vacancy and interstitial contributions, related to AsV and As i defects, respectively. Arsenic reactions are and I +As + As + i I +As + As i V +As + AsV + V +As + AsV V +As + AsV (16) (17) where we are also assuming that As + is immobile and always ionized.

7 7 Arsenic diffusion will have all previously mentioned contributions D(As) D(AsV + ) [AsV + ] [As + ] + D(As + i ) [As+ i ] [As + ] + D(AsV ) [AsV ] [As + ] + D(As i ) [As i ] [As + ] + D(AsV ) [AsV ] [As + ] which, in continuum models is usually reduced to 31 : (18) D(As) = [f [ I S I (1 f I )S V ] ( ) ] 2 D X (As) + D M (As) n n n i + D MM (As) n i, (19) f I being the fraction of interstitialassisted diffusion. Notice, however, that this continuum description conveys several simplifying assumptions compared to Eq. 18. In the first place, the common assumption that D X and D M fit an Arrhenius plot is only true if the contributions of AsV + and As + i have the same activation energy, and the same has to be true for the AsV, As i contributions. More importantly, Eq. 19 assumes that the interstitial fraction, f I is independent of the Fermi level (i.e. the same for the three charge states), and is also independent of the temperature. These assumptions reduce the range of applicability of Eq. 19. Our parameter set for As is reported in Table I. These parameters fit the equilibrium As diffusion reported by Ref. 2. The binding energy (1.3 ev) and migration energy used for AsV compares very well with abinitio calculations. 32 The value of e AsV (, ) is from Ref. 2. The activation energy of f i is the same than the value in Ref. 33. Figure 7 shows experimental diffusivity (symbols) reported in Ref. 2 for different concentrations and temperatures, compared with our calculated values. We have taken into account the field enhancement factor h. 1 Figure 8 shows the good agreement between the differential equationbased model and our atomistic simulations for the case of Arsenic indiffusion for both intrinsic and extrinsic conditions. The effect of Fermilevel is evident in the obtained box like shape profile for extrinsic diffusion. The comparison made in Figs. 7 and 8 validates the parameter translation between atomistic and continuum formulation (Eq. 15 and equivalent for As). V. DOPANT LONG HOPS INVOLVING SEVERAL CHARGE STATES In systems where diffusion proceeds via an intermediate migrating species the shape of the diffusion profiles of dopants can be substantially different, even though the standard deviations of the profiles are the same. 34,35 This is because the shape is controlled by the value of the long hop distance, Λ, (distance traveled by a point defect pair before breaking up), which is given by 35,36 1 ν m Λ = λ, (2) 6 ν bk D As (cm 2 /s) o C 15 o C 11 o C 12 o C As concentration (cm 3 ) FIG. 7: Arsenic diffusion dependence on the temperature and dopant concentration. Symbols: experimental data (Ref. 2). Lines: Calculated values (see text). Normalized As concentration Temp 8 o C n=n i n=2n i Normalized depth x/2[d * (As)t] 1/2 FIG. 8: Normalized Arsenic concentration profiles under intrinsic and extrinsic (n = 2n i) conditions for 8 o C. Lines: calculated within the continuum framework. Symbols: kmc simulations (squares: s, circles: s, triangles: 1 5 s). In order to do an even comparison, Maxwell Boltzmann statistics has been used in our simulation. taking for ν m and ν bk their average charge states. In the above mentioned case of a, Eq. 2 becomes Λ = λ 1 6 ν m (B i )[B i ] + ν m(b i )[ ] + ν m(b + i )[B+ i ] ν bk (B i )[B i ] + ν bk(b i )[ ]

8 8 Long hop distance Λ (nm) Temperature o C Experimental Intrinsic N D =1x1 17 N A =1x /T (K) FIG. 9: Arrhenius plot for long hop distance (Λ). Lines: values calculated using our parameter set for intrinsic, n doped and pdoped silicon. Symbols: experimental values in quasiintrinsic conditions. 25,34,37 which using Eq. 1 and equivalent can be written as 1 Λ = λ 6 ν m (B i ) [B i ] [B ] + ν m(b i ) [ ] [B ] + ν m(b + i ) [B+ i ] [B ] v capt (ν m (I )[I ] + ν m (I + )[I + ]) (21) and, finally using Eqs. 3 and 13 Λ = λ λ D(B) 6v capt{d(i )[I ]+D(I + )[I + ]} D (B) 6v captdc (I). The last equality assumes that the I contribution is negligible. DC (I) is the equilibrium transport capacity of interstitials. With the values we are using, Λ p/n i for e F e i. The temperature dependence of Λ for boron, using the parameters of table I is displayed in Fig. 9, both for intrinsic and doped silicon, and compared with experimental values for intrinsic materials. 34,37 It is interesting to note that the concentrations of the different charge states of interstitials (namely I + and I ) do not directly affect boron diffusivity (see equations 13 and 15). This could suggest that, as a simplifying approximation, one can neglect the presence of I and I +. However, Eq. 21 shows that, by doing so, an incorrectly large Λ value could be obtained for extrinsic materials. In fact, the magnitude of D(B) is governed by the ν m (B j i )[Bj i ]/[B ] terms, but how Gaussian the diffusion profile is, depends also on the ν m (I j )[I j ] terms. VI. AN EXAMPLE: A COMPLEX SCENARIO One of the reasons for developing the detailed modelling of charge effects presented in this work is that, in the complex processing scenarios which are now common place in advanced semiconductor manufacturing, the dominant mechanisms may not be apparent or, even worse, one can be misled by intuition. As an example, Fig. 1 corresponds to a typical 1 kev, cm 2 As + implant onto a cm 3 uniformly B doped substrate followed by a 1 min., 75 C anneal. This apparently simple experiment involves a number of different mechanisms and the simulation will only be predictive against changes in the processing conditions if each and every mechanism is correctly implemented. Namely, the simulator accumulates damage (taking into account the dose rate and implant temperature) and correctly predicts the amorphization of the top 75 nm layer and the electrical deactivation of the dopants in the damaged regions. Recrystallization occurs during the simulation of the temperature ramp up. In agreement with experimental evidence the simulated recrystallization front partially sweeps B and As, and deposits electrically active dopants up to a maximum level, depositing the rest as small defectdopant clusters. In the simulation, the EOR interstitial clusters evolve to {311} defects and, eventually to dislocation loops. The presence of the loops lowers dramatically the interstitial supersaturation and slows down transient enhanced diffusion (TED). During TED, s depleted from the junction and piles up as it enters the N side. However, it is interesting to remark that this apparent electric drift effect was actually associated to a net flux of the neutral Bi, maybe against simple intuition. Namely, the gradient of e F produces a gradient of [Bi ]/[B ] and, in consequence, a diffusion flux of Bi toward the Nregion that tends to homogenize [Bi ]. Boron pileup in the Asrich region is a result of the lower value of D(B) in Ntype materials (See Eq. 14). The Figure shows experimental results 38 as symbols, and simulation results as lines. The agreement is good, taking into account the number of mechanisms involved in the atomistic simulation as described above. 39 VII. CONCLUSIONS In this work an accurate, physicallybased atomistic modeling of Fermilevel effects of species diffusing in Silicon has been presented. This model takes into account the charge reactions and electric bias dependency with Fermilevel, pairing and breakup reactions between particles, clustering dopant activation and deactivation and the Fermilevel dependent solubility. It also includes degenerate FermiDirac statistics, bandgap narrowing and damageinduced electrical compensation. The presented model, in particular Eq. 15, establishes a bridge between atomistic kmc and continuum approaches for Fermilevel dependent diffusivity. From

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